Hard to tell because they don't provide a schematic of the board or of a typical channel lay out.There are two issues to consider.

1. Do the channel input pins drive a opto isolator and/or switching transistor to activate the relay coil(s). Most do but that is hard to determine from that picture, but there does seem to be some 4 pin IC device assigned to each relay position. If that is the case then there is no issue with an arduino output pin being able to drive a channel input pin. If not an arduino output pin cannot provide 90MA of current to turn on the relay.

2. 5vdc power for the relay coils has to come from somewhere and if you require that all 8 channels might have to be turned on in any situation that would be too much current demand for the arduino shield 5V pin, and an independent 5vdc voltage source would have to be used that is rated for the total current demand of the relay board.

The 2nd photo shows 8 components at the connector, which are probably resistors.And each relay has a component, probably a transistor.

So yeah, you can measure the current drawn per input at that input to see if it's Arduino compatible, and the total current drawn by the board in case all relays are enabled.Last one is probably somewhere close to 750 mA.

Have a look at "blink without delay".Did you connect the grounds ?Je kunt hier ook in het Nederlands terecht: http://arduino.cc/forum/index.php/board,77.0.html

You can clearly see the transistors. So yes, you will be able to switch the relays without using any external components.Beware that, if you want to switch all relays at once, you will create quite a current-peak. It would be wise to place a capacitor of 470uF to 2200uF on the 5V pins close to the relay board. Otherwise, this current-peak may create some noise that crashes the Arduino or it crashes other things attached to the 5V line (sensors?)